@article{nguyen_tanizaki_unsal_2023, title={Study of gapped phases of 4d gauge theories using temporal gauging of the Z(N) 1-form symmetry}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP08(2023)013}, abstractNote={A bstract To study gapped phases of 4d gauge theories, we introduce the temporal gauging of ℤ N 1-form symmetry in 4d quantum field theories (QFTs), thereby defining effective 3d QFTs with $$ \overset{\sim }{\mathbb{Z}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>ℤ</mml:mi> <mml:mo>~</mml:mo> </mml:mover> </mml:math> N × ℤ N 1-form symmetry. In this way, spatial fundamental Wilson and ’t Hooft loops are simultaneously genuine line operators. Assuming a mass gap and Lorentz invariant vacuum of the 4d QFT, the $$ \overset{\sim }{\mathbb{Z}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>ℤ</mml:mi> <mml:mo>~</mml:mo> </mml:mover> </mml:math> N × ℤ N symmetry must be spontaneously broken to an order- N subgroup H , and we can classify the 4d gapped phases by specifying H . This establishes the 1-to-1 correspondence between the two classification schemes for gapped phases of 4d gauge theories: one is the conventional Wilson-’t Hooft classification, and the other is the modern classification using the spontaneous breaking of 4d 1-form symmetry enriched with symmetry-protected topological states.}, number={8}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Nguyen, Mendel and Tanizaki, Yuya and Unsal, Mithat}, year={2023}, month={Aug} }
 @article{nguyen_tanizaki_unsal_2023, title={Winding ? and destructive interference of instantons}, ISSN={["1029-8479"]}, DOI={10.1007/JHEP09(2023)033}, abstractNote={A bstract While the θ dependence of field theories is 2 π periodic, the ground-state wavefunctions at θ and θ + 2 π often belong to different classes of symmetry-protected topological states. When this is the case, a continuous change of the θ parameter can introduce an interface that supports a nontrivial field theory localized on the wall. We consider the 2d ℂ P N −1 sigma model as an example and construct a weak-coupling setup of this interface theory by considering the small S 1 compactification with nonzero winding θ parameter and a suitable symmetry-twisted boundary condition. This system has N classical vacua connected by fractional instantons, but the anomaly constraint tells us that the fractional-instanton amplitudes should vanish completely to have N -fold degeneracy at the quantum level. We show how this happens in this purely bosonic system, uncovering that the integration over the zero modes annihilates the fractional instanton amplitudes, in sharp contrast to what happens when the θ angle is constant. Moreover, we provide another explanation of this selection rule by showing that the N perturbative vacua acquire different charges under the global symmetry with the activation of the winding θ angle. We also demonstrate a similar destructive interference between instanton effects in the ℂ P N −1 quantum mechanics with the Berry phase.}, number={9}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Nguyen, Mendel and Tanizaki, Yuya and Unsal, Mithat}, year={2023}, month={Sep} }
 @article{tanizaki_unsal_2022, title={Center vortex and confinement in Yang Mills theory and QCD with anomaly-preserving compactifications}, volume={2022}, ISSN={["2050-3911"]}, url={http://dx.doi.org/10.1093/ptep/ptac042}, DOI={10.1093/ptep/ptac042}, abstractNote={We construct an anomaly-preserving compactification of 4d gauge theories, including $SU(N)$ Yang-Mills theory, $\mathcal{N}=1$ supersymmetric Yang-Mills theory, and QCD, down to 2d by turning on 't Hooft flux through $T^2$. It provides a new framework to analytically calculate nonperturbative properties such as confinement, chiral symmetry breaking, and multi-branch structure of vacua. We give the semiclassical description of these phenomena based on the center vortex and show that it enjoys the same anomaly matching condition with the original $4$d gauge theory. We conjecture that the weak-coupling vacuum structure on small $T^2 \times \mathbb{R}^2$ is adiabatically connected to the strong-coupling regime on $\mathbb{R}^4$ without any phase transitions. In QCD with fundamental quarks as well, we can turn on 't Hooft flux either by activating $SU(N_f)_{\mathrm{V}}$ symmetry twist for $N_f=N$ flavors or by introducing a magnetic flux of baryon number $U(1)_{\mathrm{B}}$ for arbitrary $N_f$ flavors. In both cases, the weak-coupling center-vortex theory gives the prediction consistent with chiral Lagrangian of $4$d QCD.}, number={4}, journal={PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS}, publisher={Oxford University Press (OUP)}, author={Tanizaki, Yuya and Unsal, Mithat}, year={2022}, month={Apr} }
 @article{honda_itou_tanizaki_2022, title={DMRG study of the higher-charge Schwinger model and its ’t Hooft anomaly}, volume={11}, url={http://inspirehep.net/record/2163166}, DOI={10.1007/JHEP11(2022)141}, abstractNote={A bstract The charge- q Schwinger model is the (1 + 1)-dimensional quantum electrodynamics (QED) with a charge- q Dirac fermion. It has the ℤ q 1-form symmetry and also enjoys the ℤ q chiral symmetry in the chiral limit, and there is a mixed ’t Hooft anomaly between those symmetries. We numerically study the charge- q Schwinger model in the lattice Hamiltonian formulation using the density-matrix renormalization group (DMRG). When applying DMRG, we map the Schwinger model to a spin chain with nonlocal interaction via Jordan-Wigner transformation, and we take the open boundary condition instead of the periodic one to make the Hilbert space finite-dimensional. When computing the energy density or chiral condensate, we find that using local operators significantly reduces the boundary effect compared with the computation of corresponding extensive quantities divided by the volume. To discuss the consequence of the ’t Hooft anomaly, we carefully treat the renormalization of the chiral condensates, and then we confirm that Wilson loops generate the discrete chiral transformations in the continuum limit.}, journal={JHEP}, author={Honda, Masazumi and Itou, Etsuko and Tanizaki, Yuya}, year={2022}, month={Nov}, pages={141} }
 @article{fukushima_shimazaki_tanizaki_2022, title={Exploring the θ-vacuum structure in the functional renormalization group approach}, volume={04}, url={http://inspirehep.net/record/2023555}, DOI={10.1007/JHEP04(2022)040}, abstractNote={We investigate the $\theta$-vacuum structure and the 't Hooft anomaly at $\theta=\pi$ in a simple quantum mechanical system on $S^1$ to scrutinize the applicability of the functional renormalization group (fRG) approach. Even though the fRG is an exact formulation, a naive application of the fRG equation would miss contributions from the $\theta$ term due to the differential nature of the formulation. We first review this quantum mechanical system on $S^1$ that is solvable with both the path integral and the canonical quantization. We discuss how to construct the quantum effective action including the $\theta$ dependence. Such an explicit calculation poses a subtle question of whether a Legendre transform is well defined or not for general systems with the sign problem. We then consider a deformed theory to relax the integral winding by introducing a wine-bottle potential with the finite depth $\propto g$, so that the original $S^1$ theory is recovered in the $g\to\infty$ limit. We numerically solve the energy spectrum in the deformed theory as a function of $g$ and $\theta$ in the canonical quantization. We test the efficacy of the simplest local potential approximation (LPA) in the fRG approach and find that the correct behavior of the ground state energy is well reproduced for small $\theta$. When the energy level crossing is approached, the LPA flow breaks down and fails in describing the ground state degeneracy expected from the 't Hooft anomaly. We finally turn back to the original theory and discuss an alternative formulation using the Villain lattice action. The analysis with the Villain lattice at $\theta=\pi$ indicates that the nonlocality of the effective action is crucial to capture the level crossing behavior of the ground states.}, journal={JHEP}, author={Fukushima, Kenji and Shimazaki, Takuya and Tanizaki, Yuya}, year={2022}, month={Apr}, pages={040} }
 @article{hayashi_tanizaki_2022, title={Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly}, volume={2022}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85135228761&partnerID=MN8TOARS}, DOI={10.1007/JHEP08(2022)036}, abstractNote={A bstract We study properties of self-duality symmetry in the Cardy-Rabinovici model. The Cardy-Rabinovici model is the 4d U(1) gauge theory with electric and magnetic matters, and it enjoys the SL(2 , ℤ) self-duality at low-energies. SL(2 , ℤ) self-duality does not realize in a naive way, but we notice that the ST p duality transformation becomes the legitimate duality operation by performing the gauging of ℤ N 1-form symmetry with including the level- p discrete topological term. Due to such complications in its realization, the fusion rule of duality defects becomes a non-group-like structure, and thus the self-duality symmetry is realized as a non-invertible symmetry. Moreover, for some fixed points of the self-duality, the duality symmetry turns out to have a mixed gravitational anomaly detected on a K 3 surface, and we can rule out the trivially gapped phase as a consequence of anomaly matching. We also uncover how the conjectured phase diagram of the Cardy-Rabinovici model satisfies this new anomaly matching condition.}, number={8}, journal={Journal of High Energy Physics}, author={Hayashi, Y. and Tanizaki, Y.}, year={2022} }
 @article{tanizaki_unsal_2022, title={Semiclassics with 't Hooft flux background for QCD with 2-index quarks}, volume={08}, ISSN={["1029-8479"]}, url={http://inspirehep.net/record/2086495}, DOI={10.1007/JHEP08(2022)038}, abstractNote={We study quantum chromodynamics including the two-index symmetric or anti-symmetric quark (QCD(Sym/ASym)) on small $\mathbb{R}^2\times T^2$ with a suitable magnetic flux. We first discuss the 't Hooft anomaly of these theories and claim that discrete chiral symmetry should be spontaneously broken completely to satisfy the anomaly matching condition. The $T^2$ compactification with the magnetic flux preserves the 't Hooft anomaly, and the $2$d effective theory is constrained by the same anomaly of $4$d QCD(Sym/ASym). We demonstrate the spontaneous breakdown of chiral symmetry using the dilute gas of center vortices, which confirms the prediction of the 't Hooft anomaly. We also find that each vacuum maintains the charge conjugation symmetry, and this gives affirmative support for the nonperturbative large-$N$ orientifold equivalence between QCD(Sym/ASym) and $\mathcal{N}=1$ supersymmetric $SU(N)$ Yang-Mills theory.}, number={8}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Tanizaki, Yuya and Unsal, Mithat}, year={2022}, month={Aug} }
 @article{honda_itou_kikuchi_tanizaki_2021, title={Negative string tension of higher-charge Schwinger model via digital quantum simulation}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85118645604&partnerID=MN8TOARS}, journal={arXiv}, author={Honda, M. and Itou, E. and Kikuchi, Y. and Tanizaki, Y.}, year={2021} }
 @article{nguyen_tanizaki_ünsal_2021, title={Non-invertible 1-form symmetry and Casimir scaling in 2d Yang-Mills theory}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85106167565&partnerID=MN8TOARS}, journal={arXiv}, author={Nguyen, M. and Tanizaki, Y. and Ünsal, M.}, year={2021} }
 @article{nguyen_tanizaki_unsal_2021, title={Noninvertible 1-form symmetry and Casimir scaling in 2D Yang-Mills theory}, volume={104}, ISSN={["2470-0029"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85114421307&partnerID=MN8TOARS}, DOI={10.1103/PhysRevD.104.065003}, abstractNote={Pure Yang-Mills theory in 2 spacetime dimensions shows exact Casimir scaling. Thus there are infinitely many string tensions, and this has been understood as a result of non-propagating gluons in 2 dimensions. From ordinary symmetry considerations, however, this richness in the spectrum of string tensions seems mysterious. Conventional wisdom has it that it is the center symmetry that classifies string tensions, but being finite it cannot explain infinitely many confining strings. In this note, we resolve this discrepancy between dynamics and kinematics by pointing out the existence of a non-invertible 1-form symmetry, which is able to distinguish Wilson loops in different representations. We speculate on possible implications for Yang-Mills theories in 3 and 4 dimensions.}, number={6}, journal={PHYSICAL REVIEW D}, author={Nguyen, Mendel and Tanizaki, Yuya and Unsal, Mithat}, year={2021}, month={Sep} }
 @article{nguyen_tanizaki_ünsal_2021, title={Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond $N$-ality}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85101229833&partnerID=MN8TOARS}, journal={arXiv}, author={Nguyen, M. and Tanizaki, Y. and Ünsal, M.}, year={2021} }
 @article{nguyen_tanizaki_unsal_2021, title={Semi-Abelian gauge theories, non-invertible symmetries, and string tensions beyond N-ality}, volume={03}, ISSN={["1029-8479"]}, url={http://inspirehep.net/record/1839639}, DOI={10.1007/JHEP03(2021)238}, abstractNote={A bstract We study a 3d lattice gauge theory with gauge group U(1) N− 1 ⋊ S N , which is obtained by gauging the S N global symmetry of a pure U(1) N− 1 gauge theory, and we call it the semi-Abelian gauge theory. We compute mass gaps and string tensions for both theories using the monopole-gas description. We find that the effective potential receives equal contributions at leading order from monopoles associated with the entire SU( N ) root system. Even though the center symmetry of the semi-Abelian gauge theory is given by ℤ N , we observe that the string tensions do not obey the N -ality rule and carry more detailed information on the representations of the gauge group. We find that this refinement is due to the presence of non-invertible topological lines as a remnant of U(1) N− 1 one-form symmetry in the original Abelian lattice theory. Upon adding charged particles corresponding to W -bosons, such non-invertible symmetries are explicitly broken so that the N -ality rule should emerge in the deep infrared regime.}, number={3}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Nguyen, Mendel and Tanizaki, Yuya and Unsal, Mithat}, year={2021}, month={Mar} }
 @article{takahashi_tanizaki_2021, title={Sigma-model analysis of SU(3) antiferromagnetic spins on the triangular lattice}, volume={104}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85122103042&partnerID=MN8TOARS}, DOI={10.1103/PhysRevB.104.235152}, abstractNote={Using field-theoretic techniques, we study the $\mathrm{SU}(3)$ analog of antiferromagnetic Heisenberg spin model on the triangular lattice putting the $p$-box symmetric representation on each site. Taking the large-$p$ limit, we show that the low-energy effective theory is described by a $(2+1)$-dimensional relativistic $\mathrm{SU}(3)/\mathrm{U}{(1)}^{2}$ nonlinear sigma model. Since the target space has a nontrivial homotopy ${\ensuremath{\pi}}_{2}(\mathrm{SU}(3)/\mathrm{U}{(1)}^{2})\ensuremath{\simeq}{\mathbb{Z}}^{2}$, this model has two kinds of magnetic skyrmions, which can be created and annihilated by monopole instantons. By careful analysis of the Wess-Zumino term in the spin coherent path integral, we compute the Berry phase for these monopoles and it produces the destructive interference. This restricts possible perturbations of the effective Lagrangian by monopole operators, and we see that the valence-bond-solid (VBS) phase should have degenerate ground states when $p\ensuremath{\notin}3\mathbb{Z}$. We also compute 't Hooft anomalies to constrain possible phases of this system, and a direct phase transition between N\'eel and VBS phases is supported from the anomaly matching.}, number={23}, journal={Physical Review B}, author={Takahashi, I. and Tanizaki, Y.}, year={2021} }
 @article{takahashi_tanizaki_2021, title={Sigma-model analysis of SU(3) antiferromagnetic spins on the triangular lattice}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85115844171&partnerID=MN8TOARS}, journal={arXiv}, author={Takahashi, I. and Tanizaki, Y.}, year={2021} }
 @article{kobayashi_lee_shiozaki_tanizaki_2021, title={Topological terms of (2+1)d flag-manifold sigma models}, volume={2021}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85112854890&partnerID=MN8TOARS}, DOI={10.1007/JHEP08(2021)075}, abstractNote={A bstract We examine topological terms of (2 + 1)d sigma models and their consequences in the light of classifications of invertible quantum field theories utilizing bordism groups. In particular, we study the possible topological terms for the U( N ) / U(1) N flag-manifold sigma model in detail. We argue that the Hopf-like term is absent, contrary to the expectation from a nontrivial homotopy group π 3 (U( N ) / U(1) N ) = ℤ, and thus skyrmions cannot become anyons with arbitrary statistics. Instead, we find that there exist $$ \frac{N\left(N-1\right)}{2}-1 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mrow> <mml:mi>N</mml:mi> <mml:mfenced> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mn>2</mml:mn> </mml:mfrac> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:math> types of Chern-Simons terms, some of which can turn skyrmions into fermions, and we write down explicit forms of effective Lagrangians.}, number={8}, journal={Journal of High Energy Physics}, author={Kobayashi, Ryohei and Lee, Yasunori and Shiozaki, Ken and Tanizaki, Yuya}, year={2021}, pages={075} }
 @article{kobayashi_lee_shiozaki_tanizaki_2021, title={Topological terms of (2+1)d flag-manifold sigma models}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85103025056&partnerID=MN8TOARS}, journal={arXiv}, author={Kobayashi, R. and Lee, Y. and Shiozaki, K. and Tanizaki, Y.}, year={2021} }
 @article{cherman_jacobson_tanizaki_ünsal_2020, title={Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD}, volume={8}, url={http://inspirehep.net/record/1751322}, DOI={10.21468/SciPostPhys.8.5.072}, abstractNote={We show that 2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>2</mml:mn></mml:math> d adjoint QCD, an SU(N) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:math> gauge theory with one massless adjoint Majorana fermion, has a variety of mixed ’t Hooft anomalies. The anomalies are derived using a recent mod 2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>2</mml:mn></mml:math> index theorem and its generalization that incorporates ’t Hooft flux. Anomaly matching and dynamical considerations are used to determine the ground-state structure of the theory. The anomalies, which are present for most values of N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math> , are matched by spontaneous chiral symmetry breaking. We find that massless 2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>2</mml:mn></mml:math> d adjoint QCD confines for N >2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>N</mml:mi><mml:mo>></mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> , except for test charges of N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math> -ality N/2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>N</mml:mi><mml:mi>/</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:math> , which are deconfined. In other words, \mathbb Z_N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mstyle mathvariant="double-struck"><mml:mi>ℤ</mml:mi></mml:mstyle><mml:mi>N</mml:mi></mml:msub></mml:math> center symmetry is unbroken for odd N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math> and spontaneously broken to \mathbb Z_{N/2} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mstyle mathvariant="double-struck"><mml:mi>ℤ</mml:mi></mml:mstyle><mml:mrow><mml:mi>N</mml:mi><mml:mi>/</mml:mi><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> for even N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math> . All of these results are confirmed by explicit calculations on small \mathbb{R}\times S^1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mstyle mathvariant="double-struck"><mml:mi>ℝ</mml:mi></mml:mstyle><mml:mo>×</mml:mo><mml:msup><mml:mi>S</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:mrow></mml:math> . We also show that this non-supersymmetric theory exhibits exact Bose-Fermi degeneracies for all states, including the vacua, when N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math> is even. Furthermore, for most values of N <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math> , 2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>2</mml:mn></mml:math> d massive adjoint QCD describes a non-trivial symmetry-protected topological (SPT) phase of matter, including certain cases where the number of interacting Majorana fermions is a multiple of 8 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>8</mml:mn></mml:math> . As a result, it fits into the classification of (1+1) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo stretchy="false" form="prefix">(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false" form="postfix">)</mml:mo></mml:mrow></mml:math> d SPT phases of interacting Majorana fermions in an interesting way.}, number={5}, journal={SciPost Phys.}, author={Cherman, Aleksey and Jacobson, Theodore and Tanizaki, Yuya and Ünsal, Mithat}, year={2020}, month={May}, pages={072} }
 @article{chen_fukushima_nishimura_tanizaki_2020, title={Deconfinement and CP breaking at θ=π in Yang-Mills theories and a novel phase for SU(2)}, volume={102}, url={http://inspirehep.net/record/1798942}, DOI={10.1103/physrevd.102.034020}, abstractNote={We discuss the deconfinement and the $\mathcal{C}\mathcal{P}$-breaking phase transitions at $\ensuremath{\theta}=\ensuremath{\pi}$ in Yang-Mills theories. The 't Hooft anomaly matching prohibits the confined phase with $\mathcal{C}\mathcal{P}$ symmetry and requires ${T}_{\mathrm{dec}}(\ensuremath{\theta}=\ensuremath{\pi})\ensuremath{\le}{T}_{\mathrm{CP}}$, where ${T}_{\mathrm{dec}}(\ensuremath{\theta}=\ensuremath{\pi})$ and ${T}_{\mathrm{CP}}$ denote the deconfinement and the $\mathcal{C}\mathcal{P}$-restoration temperatures, respectively, at $\ensuremath{\theta}=\ensuremath{\pi}$. We analytically study these two phase transitions in softly broken $\mathcal{N}=1$ supersymmetric Yang-Mills theories on small ${\mathbb{R}}^{3}\ifmmode\times\else\texttimes\fi{}{S}^{1}$ with the periodic boundary condition for gluinos. For most gauge groups except SU(2) in this model, we find that the inequality is saturated, so deconfinement and $\mathcal{C}\mathcal{P}$ restoration occur simultaneously. We demonstrate special features of the SU(2) gauge theory: there is a finite window of two temperatures, ${T}_{\mathrm{dec}}(\ensuremath{\pi})<{T}_{\mathrm{CP}}$, which indicates the existence of a novel $\mathcal{C}\mathcal{P}$-broken deconfined phase. We also discuss an implication of the novel phase for domain walls and their junctions.}, number={3}, journal={Physical Review D}, publisher={American Physical Society (APS)}, author={Chen, Shi and Fukushima, Kenji and Nishimura, Hiromichi and Tanizaki, Yuya}, year={2020}, month={Aug}, pages={034020} }
 @article{chen_fukushima_nishimura_tanizaki_2020, title={Deconfinement and CP-breaking at θ = π in Yang-Mills theories and a novel phase for SU(2)}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85095233223&partnerID=MN8TOARS}, journal={arXiv}, author={Chen, S. and Fukushima, K. and Nishimura, H. and Tanizaki, Y.}, year={2020} }
 @article{furusawa_tanizaki_itou_2020, title={Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and’t Hooft Anomaly}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85094749873&partnerID=MN8TOARS}, journal={arXiv}, author={Furusawa, T. and Tanizaki, Y. and Itou, E.}, year={2020} }
 @article{furusawa_tanizaki_itou_2020, title={Finite-density massless two-color QCD at the isospin Roberge-Weiss point and the 't Hooft anomaly}, volume={2}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85098094556&partnerID=MN8TOARS}, DOI={10.1103/physrevresearch.2.033253}, abstractNote={The authors explore the symmetry properties of two color massless QCD at finite temperature and density. These properties yield exact constraints on its phase diagram at the isospin Roberge-Weiss point and also show the presence of gapless excitations localized on topological defects in symmetry-broken phases}, number={3}, journal={Physical Review Research}, publisher={American Physical Society (APS)}, author={Furusawa, Takuya and Tanizaki, Yuya and Itou, Etsuko}, year={2020}, month={Aug} }
 @article{misumi_tanizaki_2020, title={Lattice gauge theory for the Haldane conjecture and central-branch Wilson fermion}, volume={2020}, ISSN={["2050-3911"]}, url={http://dx.doi.org/10.1093/ptep/ptaa003}, DOI={10.1093/ptep/ptaa003}, abstractNote={We develop the $(1+1)$d lattice $U(1)$ gauge theory in order to define $2$-flavor massless Schwinger model, and discuss its connection with Haldane conjecture. We propose to use the central-branch Wilson fermion, which is defined by relating the mass, $m$, and the Wilson parameter, $r$, as $m+2r=0$. This setup gives two massless Dirac fermions in the continuum limit, and it turns out that no fine-tuning of $m$ is required because the extra $U(1)$ symmetry at the central branch, $U(1)_{\bar{V}}$, prohibits the additive mass renormalization. Moreover, we show that Dirac determinant is positive semi-definite and this formulation is free from the sign problem, so the Monte Carlo simulation of the path integral is possible. By identifying the symmetry at low energy, we show that this lattice model has the mixed 't Hooft anomaly between $U(1)_{\bar{V}}$, lattice translation, and lattice rotation. We discuss its relation to the anomaly of half-integer anti-ferromagnetic spin chains, so our lattice gauge theory is suitable for numerical simulation of Haldane conjecture. Furthermore, it gives new and strict understanding on parity-broken phase (Aoki phase) of $2$d Wilson fermion.}, number={3}, journal={PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS}, author={Misumi, Tatsuhiro and Tanizaki, Andyuya}, year={2020}, month={Mar} }
 @article{tanizaki_ünsal_2020, title={Modified instanton sum in QCD and higher-groups}, volume={03}, url={http://inspirehep.net/record/1768195}, DOI={10.1007/JHEP03(2020)123}, abstractNote={A bstract We consider the SU( N ) Yang-Mills theory, whose topological sectors are restricted to the instanton number with integer multiples of p . We can formulate such a quantum field theory maintaining locality and unitarity, and the model contains both 2 π -periodic scalar and 3-form gauge fields. This can be interpreted as coupling a topological theory to Yang-Mills theory, so the local dynamics becomes identical with that of pure Yang-Mills theory. The theory has not only ℤ N 1-form symmetry but also ℤ p 3-form symmetry, and we study the global nature of this theory from the recent ’t Hooft anomaly matching. The computation of ’t Hooft anomaly incorporates an intriguing higher-group structure. We also carefully examine that how such kinematical constraint is realized in the dynamics by using the large- N and also the reliable semiclassics on ℝ 3 × S 1 , and we find that the topological susceptibility plays a role of the order parameter for the ℤ p 3-form symmetry. Introducing a fermion in the fundamental or adjoint representation, we find that the chiral symmetry becomes larger than the usual case by ℤ p , and it leads to the extra p vacua by discrete chiral symmetry breaking. No dynamical domain wall can interpolate those extra vacua since such objects must be charged under the 3-form symmetry in order to match the ’t Hooft anomaly.}, number={3}, journal={JHEP}, author={Tanizaki, Yuya and Ünsal, Mithat}, year={2020}, month={Mar}, pages={123} }
 @article{honda_tanizaki_2020, title={Topological aspects of 4D Abelian lattice gauge theories with the θ parameter}, volume={2020}, url={http://dx.doi.org/10.1007/jhep12(2020)154}, DOI={10.1007/jhep12(2020)154}, abstractNote={We study a four-dimensional $U(1)$ gauge theory with the $\theta$ angle, which was originally proposed by Cardy and Rabinovici. It is known that the model has the rich phase diagram thanks to the presence of both electrically and magnetically charged particles. We discuss the topological nature of the oblique confinement phase of the model at $\theta=\pi$, and show how its appearance can be consistent with the anomaly constraint. We also construct the $SL(2,\mathbb{Z})$ self-dual theory out of the Cardy-Rabinovici model by gauging a part of its one-form symmetry. This self-duality has a mixed 't Hooft anomaly with gravity, and its implications on the phase diagram is uncovered. As the model shares the same global symmetry and 't Hooft anomaly with those of $SU(N)$ Yang-Mills theory, studying its topological aspects would provide us more hints to explore possible dynamics of non-Abelian gauge theories with nonzero $\theta$ angles.}, number={12}, journal={Journal of High Energy Physics}, publisher={Springer Science and Business Media LLC}, author={Honda, Masazumi and Tanizaki, Yuya}, year={2020}, month={Dec}, pages={154} }
 @article{honda_tanizaki_2020, title={Topological aspects of 4D Abelian lattice gauge theories with the θ parameter}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85098375063&partnerID=MN8TOARS}, journal={arXiv}, author={Honda, M. and Tanizaki, Y.}, year={2020} }
 @article{sulejmanpasic_tanizaki_ünsal_2020, title={Universality between vector-like and chiral quiver gauge theories: Anomalies and domain walls}, volume={06}, url={http://inspirehep.net/record/1792165}, DOI={10.1007/JHEP06(2020)173}, abstractNote={We study low-energy dynamics of $[SU(N)]^K$ chiral quiver gauge theories in connection with $\mathcal{N}=1$ super Yang-Mills (SYM) theory, and quantum chromodynamics with bi-fundamental fermions (QCD(BF)). These theories can be obtained by $\mathbb{Z}_K$ orbifold projections of $\mathcal{N}=1$ $SU(NK)$ SYM theory, but the perturbative planar equivalence does not extend nonperturbatively for $K\ge 3$. In order to study low-energy behaviors, we analyze these systems using 't~Hooft anomaly matching and reliable semiclassics on $\mathbb{R}^3\times S^1$. Thanks to 't~Hooft anomaly that involves $1$-form center symmetry and discrete chiral symmetry, we predict that chiral symmetry must be spontaneously broken in the confinement phase, and there exist $N$ vacua. Theories with even $K$ possess a physical $\theta$ angle despite the presence of massless fermions, and we further predict the $N$-branch structure associated with it; the number of vacua is enhanced to $2N$ at $\theta=\pi$ due to spontaneous $CP$ breaking. Both of these predictions are explicitly confirmed by reliable semiclassics on $\mathbb{R}^3\times S^1$ with the double-trace deformation. Symmetry and anomaly of odd-$K$ theories are the same as those of the ${\cal N}=1$ SYM, and the ones of even-$K$ theories are same as those of QCD(BF). We unveil why there exists universality between vector-like and chiral quiver theories, and conjecture that their ground states can be continuously deformed without quantum phase transitions. We briefly discuss anomaly inflow on the domain walls connecting the vacua of the theory and possible anomaly matching scenarios.}, number={6}, journal={JHEP}, author={Sulejmanpasic, Tin and Tanizaki, Yuya and Ünsal, Mithat}, year={2020}, month={Jun}, pages={173} }
 @article{sulejmanpasic_tanizaki_ünsal_2020, title={Universality between vector-like and chiral quiver gauge theories: Anomalies and domain walls}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85095106160&partnerID=MN8TOARS}, journal={arXiv}, author={Sulejmanpasic, T. and Tanizaki, Y. and Ünsal, M.}, year={2020} }
 @article{cherman_jacobson_tanizaki_ünsal_2019, title={Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85094077070&partnerID=MN8TOARS}, journal={arXiv}, author={Cherman, A. and Jacobson, T. and Tanizaki, Y. and Ünsal, M.}, year={2019} }
 @article{hirono_tanizaki_2019, title={Effective gauge theories of superfluidity with topological order}, volume={2019}, ISSN={["1029-8479"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85068917931&partnerID=MN8TOARS}, DOI={10.1007/JHEP07(2019)062}, abstractNote={We discuss the low-energy dynamics of superfluidity with topological order in $(3+1)$ spacetime dimensions. We generalize a topological $BF$ theory by introducing a non-square $K$ matrix, and this generalized $BF$ theory can describe massless Nambu-Goldstone bosons and anyonic statistics between vortices and quasiparticles. We discuss the general structure of discrete and continuous higher-form symmetries in this theory, which can be used to classify quantum phases. We describe how to identify the appearance of topological order in such systems and discuss its relation to a mixed 't Hooft anomaly between discrete higher-form symmetries. We apply this framework to the color-flavor locked phase of dense QCD, which shows anyonic particle-vortex statistics while no topological order appears. An explicit example of superfluidity with topological order is discussed.}, number={7}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Hirono, Yuji and Tanizaki, Yuya}, year={2019}, month={Jul} }
 @article{hirono_tanizaki_2019, title={Effective gauge theories of superfluidity with topological order}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85094084730&partnerID=MN8TOARS}, journal={arXiv}, author={Hirono, Y. and Tanizaki, Y.}, year={2019} }
 @article{misumi_tanizaki_unsal_2019, title={Fractional theta angle, 't Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model}, volume={2019}, ISSN={["1029-8479"]}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85068760265&partnerID=MN8TOARS}, DOI={10.1007/JHEP07(2019)018}, abstractNote={A bstract This work examines non-perturbative dynamics of a 2-dimensional QFT by using discrete ’t Hooft anomaly, semi-classics with circle compactification and bosonization. We focus on charge- q N -flavor Schwinger model, and also Wess-Zumino-Witten model. We first apply the recent developments of discrete ’t Hooft anomaly matching to theories on ℝ 2 and its compactification to ℝ× S L 1 . We then compare the ’t Hooft anomaly with dynamics of the models by explicitly constructing eigenstates and calculating physical quantities on the cylinder spacetime with periodic and flavor-twisted boundary conditions. We find different boundary conditions realize different anomalies. Especially under the twisted boundary conditions, there are Nq vacua associated with discrete chiral symmetry breaking. Chiral condensates for this case have fractional θ dependence e i θ / Nq , which provides the Nq -branch structure with soft fermion mass. We show that these behaviors at a small circumference cannot be explained by usual instantons but should be understood by “quantum” instantons, which saturate the BPS bound between classical action and quantum-induced effective potential. The effects of the quantum-instantons match the exact results obtained via bosonization within the region of applicability of semi-classics. We also argue that large- N limit of the Schwinger model with twisted boundary conditions satisfy volume independence.}, number={7}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Misumi, Tatsuhiro and Tanizaki, Yuya and Unsal, Mithat}, year={2019}, month={Jul} }
 @article{misumi_tanizaki_ünsal_2019, title={Fractional θ angle,’t Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85093811712&partnerID=MN8TOARS}, journal={arXiv}, author={Misumi, T. and Tanizaki, Y. and Ünsal, M.}, year={2019} }
 @article{nishimura_tanizaki_2019, title={High-temperature domain walls of QCD with imaginary chemical potentials}, volume={06}, ISSN={["1029-8479"]}, url={http://inspirehep.net/record/1724461}, DOI={10.1007/JHEP06(2019)040}, abstractNote={A bstract We study QCD with massless quarks on ℝ 3 × S 1 under symmetry-twisted boundary conditions with small compactification radius, i.e. at high temperatures. Under suitable boundary conditions, the theory acquires a part of the center symmetry and it is spontaneously broken at high temperatures. We show that these vacua at high temperatures can be regarded as different symmetry-protected topological orders, and the domain walls between them support nontrivial massless gauge theories as a consequence of anomaly-inflow mechanism. At sufficiently high temperatures, we can perform the semi-classical analysis to obtain the domain-wall theory, and 2d U( N c − 1) gauge theories with massless fermions match the ’t Hooft anomaly. We perform these analysis for the high-temperature domain wall of $$ {\mathbb{Z}}_{N_{\mathrm{c}}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℤ</mml:mi> <mml:msub> <mml:mi>N</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:msub> </mml:math> - QCD and also of Roberge-Weiss phase transitions.}, number={6}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Nishimura, Hiromichi and Tanizaki, Yuya}, year={2019}, month={Jun} }
 @article{nishimura_tanizaki_2019, title={High-temperature domain walls of QCD with imaginary chemical potentials}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85094479048&partnerID=MN8TOARS}, journal={arXiv}, author={Nishimura, H. and Tanizaki, Y.}, year={2019} }
 @article{misumi_tanizaki_2019, title={Lattice gauge theory for haldane conjecture and central-branch wilson fermion}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85098339327&partnerID=MN8TOARS}, journal={arXiv}, author={Misumi, T. and Tanizaki, Y.}, year={2019} }
 @article{ünsal_tanizaki_2019, title={Modified instanton sum in QCD and higher-groups}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85093208063&partnerID=MN8TOARS}, journal={arXiv}, author={Ünsal, M. and Tanizaki, Y.}, year={2019} }
 @article{hongo_misumi_tanizaki_2019, title={Phase structure of the twisted $SU(3)/U(1)^2$ flag sigma model on $\mathbb{R}\times S^1$}, volume={02}, url={http://inspirehep.net/record/1707499}, DOI={10.1007/JHEP02(2019)070}, abstractNote={A bstract We investigate the phase structure of the compactified 2-dimensional nonlinear SU(3)/U(1) 2 flag sigma model with respect to two θ -terms. Based on the circle compactification with the ℤ 3 -twisted boundary condition, which preserves an ’t Hooft anomaly of the original uncompactified theory, we perform the semiclassical analysis based on the dilute instanton gas approximation (DIGA). We clarify classical vacua of the theory and derive fractional instanton solutions connecting these vacua. The resulting phase structure based on DIGA exhibits the quantum phase transitions and triple degeneracy at special points in the ( θ 1 , θ 2 )-plane, which is consistent with the phase diagram obtained from the anomaly matching and global inconsistency conditions. This result indicates the adiabatic continuity between the flag sigma models on ℝ 2 and ℝ × S 1 with small compactification radius. We further estimate contributions from instanton-anti-instanton configuration (bion) and show the existence of the imaginary ambiguity, which is expected to be cancelled by that of the perturbative Borel resummation.}, number={2}, journal={JHEP}, author={Hongo, Masaru and Misumi, Tatsuhiro and Tanizaki, Yuya}, year={2019}, month={Feb}, pages={070} }
 @article{hirono_tanizaki_2019, title={Quark-Hadron Continuity beyond the Ginzburg-Landau Paradigm}, volume={122}, ISSN={["1079-7114"]}, url={http://inspirehep.net/record/1705384}, DOI={10.1103/PhysRevLett.122.212001}, abstractNote={Quark-hadron continuity is a scenario in which hadronic matter is continuously connected to a color superconductor without phase transitions as the baryon chemical potential increases. This scenario is based on Landau's classification of phases, since they have the same symmetry breaking pattern. We address the question of whether this continuity is true as quantum phases of matter, which requires treatment beyond the Ginzburg-Landau description. To examine the topological nature of a color superconductor, we derive a dual effective theory for U(1) Nambu-Goldstone (NG) bosons and vortices of the color-flavor locked phase and discuss the fate of emergent higher-form symmetries. The theory has the form of a topological BF theory coupled to NG bosons, and fractional statistics of test quarks and vortices arise as a result of an emergent ${\mathbb{Z}}_{3}$ two-form symmetry. We find that this symmetry cannot be spontaneously broken, indicating that quark-hadron continuity is still a consistent scenario.}, number={21}, journal={PHYSICAL REVIEW LETTERS}, author={Hirono, Yuji and Tanizaki, Yuya}, year={2019}, month={May} }
 @article{hidaka_hirono_nitta_tanizaki_yokokura_2019, title={Topological order in a color-flavor locked phase of (3 + 1)-dimensional U(N) gauge-Higgs system}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85093431665&partnerID=MN8TOARS}, journal={arXiv}, author={Hidaka, Y. and Hirono, Y. and Nitta, M. and Tanizaki, Y. and Yokokura, R.}, year={2019} }
 @article{hidaka_hirono_nitta_tanizaki_yokokura_2019, title={Topological order in the color-flavor locked phase of a ( 3+1 )-dimensional U(N) gauge-Higgs system}, volume={100}, url={http://inspirehep.net/record/1725189}, DOI={10.1103/PhysRevD.100.125016}, abstractNote={We study a ($3+1$)-dimensional $U(N)$ gauge theory with $N$-flavor fundamental scalar fields, whose color-flavor locked (CFL) phase has topologically stable non-Abelian vortices. The $U(1)$ charge of the scalar fields must be $Nk+1$ for some integer $k$ in order for them to be in the representation of $U(N)$ gauge group. This theory has a ${\mathbb{Z}}_{Nk+1}$ one-form symmetry, and it is spontaneously broken in the CFL phase, i.e., the CFL phase is topologically ordered if $k\ensuremath{\ne}0$. We also find that the world sheet of topologically stable vortices in CFL phase can generate this one-form symmetry.}, number={12}, journal={Phys.Rev.D}, author={Hidaka, Yoshimasa and Hirono, Yuji and Nitta, Muneto and Tanizaki, Yuya and Yokokura, Ryo}, year={2019}, month={Dec}, pages={125016} }
 @article{tanizaki_sulejmanpasic_2018, title={Anomaly and global inconsistency matching: $\theta$-angles, $SU(3)/U(1)^2$ nonlinear sigma model, $SU(3)$ chains and its generalizations}, volume={98}, url={http://inspirehep.net/record/1675305}, DOI={10.1103/PhysRevB.98.115126}, abstractNote={We discuss the $SU(3)/[U(1)\times U(1)]$ nonlinear sigma model in 1+1D and, more broadly, its linearized counterparts. Such theories can be expressed as $U(1)\times U(1)$ gauge theories and therefore allow for two topological $\theta$-angles. These models provide a field theoretic description of the $SU(3)$ chains. We show that, for particular values of $\theta$-angles, a global symmetry group of such systems has a 't Hooft anomaly, which manifests itself as an inability to gauge the global symmetry group. By applying anomaly matching, the ground-state properties can be severely constrained. The anomaly matching is an avatar of the Lieb-Schultz-Mattis (LSM) theorem for the spin chain from which the field theory descends, and it forbids a trivially gapped ground state for particular $\theta$-angles. We generalize the statement of the LSM theorem and show that 't Hooft anomalies persist even under perturbations which break the spin-symmetry down to the discrete subgroup $\mathbb Z_3\times\mathbb Z_3\subset SU(3)/\mathbb Z_3$. In addition the model can further be constrained by applying global inconsistency matching, which indicates the presence of a phase transition between different regions of $\theta$-angles. We use these constraints to give possible scenarios of the phase diagram. We also argue that at the special points of the phase diagram the anomalies are matched by the $SU(3)$ Wess-Zumino-Witten model. We generalize the discussion to the $SU(N)/U(1)^{N-1}$ nonlinear sigma models as well as the 't Hooft anomaly of the $SU(N)$ Wess-Zumino-Witten model, and show that they match. Finally the $(2+1)$-dimensional extension is considered briefly, and we show that it has various 't Hooft anomalies leading to nontrivial consequences.}, number={11}, journal={Phys.Rev.B}, author={Tanizaki, Yuya and Sulejmanpasic, Tin}, year={2018}, month={Sep}, pages={115126} }
 @article{tanizaki_sulejmanpasic_2018, title={Anomaly and global inconsistency matching: Θ-angles, SU(3)=U(1)2 nonlinear sigma model, SU(3) chains and its generalizations}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85094436714&partnerID=MN8TOARS}, journal={arXiv}, author={Tanizaki, Y. and Sulejmanpasic, T.}, year={2018} }
 @article{tanizaki_2018, title={Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking}, volume={08}, url={http://inspirehep.net/record/1683303}, DOI={10.1007/JHEP08(2018)171}, abstractNote={We discuss consequences of the 't Hooft anomaly matching condition for Quantum Chromodynamics (QCD) with massless fundamental quarks. We derive the new discrete 't Hooft anomaly of massless QCD for generic numbers of color $N_\mathrm{c}$ and flavor $N_\mathrm{f}$, and an exotic chiral-symmetry broken phase without quark-bilinear condensate is ruled out from possible QCD vacua. We show that the $U(1)_\mathrm{B}$ baryon number symmetry is anomalously broken when the $(\mathbb{Z}_{2N_\mathrm{f}})_\mathrm{A}$ discrete axial symmetry and the flavor symmetry are gauged. In the ordinary chiral symmetry breaking, the Skyrmion current turns out to reproduce this 't Hooft anomaly of massless QCD. In the exotic chiral symmetry breaking, however, the anomalous breaking of $U(1)_\mathrm{B}$ does not take the correct form, and it is inconsistent with anomaly matching. This no-go theorem is based only on symmetries and anomalies, and thus has a wider range of applicability to the QCD phase diagram than the previous one obtained by QCD inequalities. Lastly, as another application, we check that duality of $\mathcal{N}=1$ supersymmetric QCD with $N_\mathrm{f}\ge N_\mathrm{c}+1$ satisfies the new anomaly matching.}, number={8}, journal={JHEP}, author={Tanizaki, Yuya}, year={2018}, month={Aug}, pages={171} }
 @article{tanizaki_2018, title={Anomaly constraint on massless QCD and the role of Skyrmions in chiral symmetry breaking}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85094302462&partnerID=MN8TOARS}, journal={arXiv}, author={Tanizaki, Y.}, year={2018} }
 @article{tanizaki_kikuchi_misumi_sakai_2018, title={Anomaly matching for the phase diagram of massless $\mathbb{Z}_N$-QCD}, volume={97}, url={http://inspirehep.net/record/1639445}, DOI={10.1103/PhysRevD.97.054012}, abstractNote={We elucidate that the phase diagram of massless $N$-flavor QCD under a ${\mathbb{Z}}_{N}$ flavor-twisted boundary condition (massless ${\mathbb{Z}}_{N}$-QCD) is constrained by a 't Hooft anomaly involving two-form gauge fields. As a consequence, massless ${\mathbb{Z}}_{N}$-QCD turns out to realize persistent order at any temperature and quark chemical potential; namely, the symmetric and gapped phase is strictly forbidden. This is the first result on the finite-$(T,\ensuremath{\mu})$ phase diagram in QCD-type theories based on anomaly matching related to center and discrete axial symmetries.}, number={5}, journal={Phys.Rev.D}, author={Tanizaki, Yuya and Kikuchi, Yuta and Misumi, Tatsuhiro and Sakai, Norisuke}, year={2018}, month={Mar}, pages={054012} }
 @article{sulejmanpasic_tanizaki_2018, title={C-P-T anomaly matching in bosonic quantum field theory and spin chains}, volume={97}, url={http://inspirehep.net/record/1653665}, DOI={10.1103/PhysRevB.97.144201}, abstractNote={We consider the $O(3)$ nonlinear sigma model with the $\theta$-term and its linear counterpart in 1+1D. The model has discrete time-reflection and space-reflection symmetries at any $\theta$, and enjoys the periodicity in $\theta\rightarrow \theta+2\pi$. At $\theta=0,\pi$ it also has a charge-conjugation $C$-symmetry. Gauging the discrete space-time reflection symmetries is interpreted as putting the theory on the nonorientable $\mathbb RP^2$ manifold, after which the $2\pi$ periodicity of $\theta$ and the $C$ symmetry at $\theta=\pi$ are lost. We interpret this observation as a mixed 't Hooft anomaly among charge-conjugation $C$, parity $P$, and time-reversal $T$ symmetries when $\theta=\pi$. Anomaly matching implies that in this case the ground state cannot be trivially gapped, as long as $C$, $P$ and $T$ are all good symmetries of the theory. We make several consistency checks with various semi-classical regimes, and with the exactly solvable XYZ model. We interpret this anomaly as an anomaly of the corresponding spin-half chains with translational symmetry, parity and time reversal (but not involving the $SO(3)$-spin symmetry), requiring that the ground state is never trivially gapped, even if $SO(3)$ spin symmetry is explicitly and completely broken. We also consider generalizations to $\mathbb{C}P^{N-1}$ models and show that the $C$-$P$-$T$ anomaly exists for even $N$.}, number={14}, journal={Phys.Rev.B}, author={Sulejmanpasic, Tin and Tanizaki, Yuya}, year={2018}, month={Apr}, pages={144201} }
 @article{sulejmanpasic_tanizaki_2018, title={C-P-T anomaly matching in bosonic quantum field theory and spin chains}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85093420369&partnerID=MN8TOARS}, journal={arXiv}, author={Sulejmanpasic, T. and Tanizaki, Y.}, year={2018} }
 @article{kozcaz_sulejmanpasic_tanizaki_unsal_2018, title={Cheshire Cat Resurgence, Self-Resurgence and Quasi-Exact Solvable Systems}, volume={364}, ISSN={["1432-0916"]}, url={http://inspirehep.net/record/1487463}, DOI={10.1007/s00220-018-3281-y}, abstractNote={We explore a one parameter $\zeta$-deformation of the quantum-mechanical Sine-Gordon and Double-Well potentials which we call the Double Sine-Gordon (DSG) and the Tilted Double Well (TDW), respectively. In these systems, for positive integer values of $\zeta$, the lowest $\zeta$ states turn out to be exactly solvable for DSG - a feature known as Quasi-Exact-Solvability (QES) - and solvable to all orders in perturbation theory for TDW. For DSG such states do not show any instanton-like dependence on the coupling constant, although the action has real saddles. On the other hand, although it has no real saddles, the TDW admits all-orders perturbative states that are not normalizable, and hence, requires a non-perturbative energy shift. Both of these puzzles are solved by including complex saddles. We show that the convergence is dictated by the quantization of the hidden topological angle. Further, we argue that the QES systems can be linked to the exact cancellation of real and complex non-perturbative saddles to all orders in the semi-classical expansion. We also show that the entire resurgence structure remains encoded in the analytic properties of the $\zeta$-deformation, even though exactly at integer values of $\zeta$ the mechanism of resurgence is obscured by the lack of ambiguity in both the Borel sum of the perturbation theory as well as the non-perturbative contributions. In this way, all of the characteristics of resurgence remains even when its role seems to vanish, much like the lingering grin of the Cheshire Cat. We also show that the perturbative series is Self-resurgent -a feature by which there is a one-to-one relation between the early terms of the perturbative expansion and the late terms of the same expansion -which is intimately connected with the Dunne-\"{U}nsal relation. We explicitly verify that this is indeed the case.}, number={3}, journal={COMMUNICATIONS IN MATHEMATICAL PHYSICS}, author={Kozcaz, Can and Sulejmanpasic, Tin and Tanizaki, Yuya and Unsal, Mithat}, year={2018}, month={Dec}, pages={835–878} }
 @article{kharzeev_kikuchi_meyer_tanizaki_2018, title={Giant photocurrent in asymmetric Weyl semimetals from the helical magnetic effect}, volume={98}, url={http://inspirehep.net/record/1652596}, DOI={10.1103/PhysRevB.98.014305}, abstractNote={We propose a type of photoresponse induced in asymmetric Weyl semimetals in an external magnetic field. In usual symmetric Weyl semimetals in a magnetic field, the particles and holes produced by an incident light in different Weyl cones have opposite helicities and hence move in opposite directions, canceling each other's contributions to the photocurrent. However this cancellation does not occur if the Weyl semimetal possesses both a broken particle-hole symmetry and a broken spatial inversion symmetry. We call the resulting generation of photocurrent the helical magnetic effect because it is induced by the helicity imbalance in a magnetic field. We find that due to the large density of states in a magnetic field, the helical magnetic effect induces a remarkable large photocurrent for incident THz frequency light. This suggests a potential application of asymmetric Weyl semimetals for creating THz photosensors.}, number={1}, journal={Phys.Rev.B}, author={Kharzeev, Dmitri E. and Kikuchi, Yuta and Meyer, Rene and Tanizaki, Yuya}, year={2018}, month={Jul}, pages={014305} }
 @article{kharzeev_kikuchi_meyer_tanizaki_2018, title={Giant photocurrent in asymmetric Weyl semimetals from the helical magnetic effect}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85093751175&partnerID=MN8TOARS}, journal={arXiv}, author={Kharzeev, D.E. and Kikuchi, Y. and Meyer, R. and Tanizaki, Y.}, year={2018} }
 @article{hongo_misumi_tanizaki_2018, title={Phase structure of the twisted SU(3)/U(1)<sup>2</sup> flag sigma model on ℝ × S<sup>1</sup>}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85094513756&partnerID=MN8TOARS}, journal={arXiv}, author={Hongo, M. and Misumi, T. and Tanizaki, Y.}, year={2018} }
 @article{dunne_tanizaki_unsal_2018, title={Quantum distillation of Hilbert spaces, semi-classics and anomaly matching}, volume={08}, ISSN={["1029-8479"]}, url={http://inspirehep.net/record/1658917}, DOI={10.1007/JHEP08(2018)068}, abstractNote={A bstract A symmetry-twisted boundary condition of the path integral provides a suitable framework for the semi-classical analysis of nonperturbative quantum field theories (QFTs), and we reinterpret it from the viewpoint of the Hilbert space. An appropriate twist with the unbroken symmetry can potentially produce huge cancellations among excited states in the state-sum, without affecting the ground states; we call this effect “quantum distillation”. Quantum distillation can provide the underlying mechanism for adiabatic continuity, by preventing a phase transition under S 1 compactification. We revisit this point via the ’t Hooft anomaly matching condition when it constrains the vacuum structure of the theory on ℝ d and upon compactification. We show that there is a precise relation between the persistence of the anomaly upon compactification, the Hilbert space quantum distillation, and the semi-classical analysis of the corresponding symmetry-twisted path integrals. We motivate quantum distillation in quantum mechanical examples, and then study its non-trivial action in QFT, with the example of the 2D Grassmannian sigma model Gr( N, M ). We also discuss the connection of quantum distillation with large- N volume independence and flavor-momentum transmutation.}, number={8}, journal={JOURNAL OF HIGH ENERGY PHYSICS}, author={Dunne, Gerald V. and Tanizaki, Yuya and Unsal, Mithat}, year={2018}, month={Aug} }
 @article{dunne_tanizaki_unsal_2018, title={Quantum distillation of Hilbert spaces, semi-classics and anomaly matching}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85093588857&partnerID=MN8TOARS}, journal={arXiv}, author={Dunne, G.V. and Tanizaki, Y. and Unsal, M.}, year={2018} }
 @article{hirono_tanizaki_2018, title={Quark-hadron continuity beyond Ginzburg-Landau paradigm}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85094511557&partnerID=MN8TOARS}, journal={arXiv}, author={Hirono, Y. and Tanizaki, Y.}, year={2018} }
 @article{tanizaki_misumi_sakai_2017, title={Circle compactification and 't Hooft anomaly}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85094235087&partnerID=MN8TOARS}, journal={arXiv}, author={Tanizaki, Y. and Misumi, T. and Sakai, N.}, year={2017} }
 @article{tanizaki_misumi_sakai_2017, title={Circle compactification and ’t Hooft anomaly}, volume={12}, url={http://inspirehep.net/record/1632455}, DOI={10.1007/JHEP12(2017)056}, abstractNote={Anomaly matching constrains low-energy physics of strongly-coupled field theories, but it is not useful at finite temperature due to contamination from high-energy states. The known exception is an 't Hooft anomaly involving one-form symmetries as in pure $SU(N)$ Yang-Mills theory at $\theta=\pi$. Recent development about large-$N$ volume independence, however, gives us a circumstantial evidence that 't Hooft anomalies can also remain under circle compactifications in some theories without one-form symmetries. We develop a systematic procedure for deriving an 't Hooft anomaly of the circle-compactified theory starting from the anomaly of the original uncompactified theory without one-form symmetries, where the twisted boundary condition for the compactified direction plays a pivotal role. As an application, we consider $\mathbb{Z}_N$-twisted $\mathbb{C}P^{N-1}$ sigma model and massless $\mathbb{Z}_N$-QCD, and compute their anomalies explicitly.}, number={12}, journal={JHEP}, author={Tanizaki, Yuya and Misumi, Tatsuhiro and Sakai, Norisuke}, year={2017}, month={Dec}, pages={056} }
 @article{kikuchi_tanizaki_2017, title={Global inconsistency, 't Hooft anomaly, and level crossing in quantum mechanics}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85093463966&partnerID=MN8TOARS}, journal={arXiv}, author={Kikuchi, Y. and Tanizaki, Y.}, year={2017} }
 @article{kikuchi_tanizaki_2017, title={Global inconsistency, ’t Hooft anomaly, and level crossing in quantum mechanics}, volume={2017}, url={http://inspirehep.net/record/1614649}, DOI={10.1093/ptep/ptx148}, abstractNote={An 't Hooft anomaly is the obstruction for gauging symmetries, and it constrains possible low-energy behaviors of quantum field theories by excluding trivial infrared theories. Global inconsistency condition is recently proposed as a milder condition but is expected to play an almost same role by comparing high symmetry points in the theory space. In order to clarify the consequence coming from this new condition, we discuss several quantum mechanical models with topological angles and explicitly compute their energy spectra. It turns out that the global inconsistency can be saturated not only by the ground-state degeneracy at either of high symmetry points but also by the level crossing (phase transition) separating those high symmetry points.}, number={11}, journal={PTEP}, author={Kikuchi, Yuta and Tanizaki, Yuya}, year={2017}, month={Nov}, pages={113B05} }
 @article{tanizaki_nishimura_verbaarschot_2017, title={Gradient flows without blow-up for Lefschetz thimbles}, volume={10}, url={http://inspirehep.net/record/1604895}, DOI={10.1007/JHEP10(2017)100}, abstractNote={We propose new gradient flows that define Lefschetz thimbles and do not blow up in a finite flow time. We study analytic properties of these gradient flows, and confirm them by numerical tests in simple examples.}, number={10}, journal={JHEP}, author={Tanizaki, Yuya and Nishimura, Hiromichi and Verbaarschot, Jacobus J.M.}, year={2017}, month={Oct}, pages={100} }
 @article{tanizaki_nishimura_verbaarschot_2017, title={Gradient flows without blow-up for Lefschetz thimbles}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85093307885&partnerID=MN8TOARS}, journal={arXiv}, author={Tanizaki, Y. and Nishimura, H. and Verbaarschot, J.J.M.}, year={2017} }
 @article{tanizaki_hatsuda_2017, title={Multi-Regulator Functional Renormalization Group for Many-Fermion Systems}, volume={26}, url={http://inspirehep.net/record/1279937}, DOI={10.1142/S0218301317400274}, abstractNote={We propose a method of multi-regulator functional renormalization group (MR-FRG) which is a novel formulation of functional renormalization group with multiple infrared (IR) regulators. It is applied to a two-component fermionic system with an attractive contact interaction to study crossover phenomena between the Bardeen–Cooper–Schrieffer (BCS) phase and the Bose–Einstein condensation (BEC) phase. To control both the fermionic one-particle excitations and the bosonic collective excitations, IR regulators are introduced, one for the fermionic two-point function and another for the four-fermion vertex. It is shown that the Nozières–Schmitt-Rink (NSR) theory, which is successful to capture qualitative features of the BCS–BEC crossover, can be derived from MR–FRG. Some aspects of MR-FRG to go beyond the NSR theory are also discussed.}, number={01n02}, journal={Int.J.Mod.Phys.E}, author={Tanizaki, Yuya and Hatsuda, Tetsuo}, year={2017}, month={Jan}, pages={1740027} }
 @article{tanizaki_tachibana_2017, title={Multi-flavor massless QED$_2$ at finite densities via Lefschetz thimbles}, volume={02}, url={http://inspirehep.net/record/1505181}, DOI={10.1007/JHEP02(2017)081}, abstractNote={We consider multi-flavor massless (1 + 1)-dimensional QED with chemical potentials at finite spatial length and the zero-temperature limit. Its sign problem is solved using the mean-field calculation with complex saddle points.}, number={2}, journal={JHEP}, author={Tanizaki, Yuya and Tachibana, Motoi}, year={2017}, month={Feb}, pages={081} }
 @article{hayata_kikuchi_tanizaki_2017, title={Topological Properties of the Chiral Magnetic Effect in Multi-Weyl Semimetals}, volume={96}, url={http://inspirehep.net/record/1516418}, DOI={10.1103/PhysRevB.96.085112}, abstractNote={We compute the chiral magnetic effect (CME) in multi-Weyl semimetals (multi-WSMs) based on the chiral kinetic theory. Multi-WSMs are WSMs with multiple monopole charges that have nonlinear and anisotropic dispersion relations near the Weyl points, and we need to extend the conventional computation of the CME in WSMs with linear dispersion relations. The topological properties of the CME in multi-WSMs are investigated in detail for not only static magnetic fields but also time-dependent (dynamic) ones. We propose an experimental setup to measure the multiple monopole charge via the topological nature hidden in the dynamic CME.}, number={8}, journal={Phys.Rev.B}, author={Hayata, Tomoya and Kikuchi, Yuta and Tanizaki, Yuya}, year={2017}, month={Aug}, pages={085112} }
 @article{hayata_kikuchi_tanizaki_2017, title={Topological properties of the chiral magnetic effect in multi-Weyl semimetals}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85093248678&partnerID=MN8TOARS}, journal={arXiv}, author={Hayata, T. and Kikuchi, Y. and Tanizaki, Y.}, year={2017} }
 @article{tanizaki_kikuchi_2017, title={Vacuum structure of bifundamental gauge theories at finite topological angles}, volume={06}, url={http://inspirehep.net/record/1598267}, DOI={10.1007/JHEP06(2017)102}, abstractNote={We discuss possible vacuum structures of SU(n) × SU(n) gauge theories with bifundamental matters at finite θ angles. In order to give a precise constraint, a mixed 't Hooft anomaly is studied in detail by gauging the center ℤ n one-form symmetry of the bifundamental gauge theory. We propose phase diagrams that are consistent with the con-straints, and also give a heuristic explanation of the result based on the dual superconductor scenario of confinement.}, number={6}, journal={JHEP}, author={Tanizaki, Yuya and Kikuchi, Yuta}, year={2017}, month={Jun}, pages={102} }
 @article{tanizaki_kikuchi_2017, title={Vacuum structure of bifundamental gauge theories at finite topological angles}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-85093405522&partnerID=MN8TOARS}, journal={arXiv}, author={Tanizaki, Y. and Kikuchi, Y.}, year={2017} }
 @article{hayata_hidaka_tanizaki_2016, title={Complex saddle points and the sign problem in complex Langevin simulation}, volume={911}, url={http://inspirehep.net/record/1403563}, DOI={10.1016/j.nuclphysb.2016.07.031}, abstractNote={We show that complex Langevin simulation converges to a wrong result, by relating it to the Lefschetz-thimble path integral, when the path-integral weight has different phases among dominant complex saddle points. Equilibrium solution of the complex Langevin equation forms local distributions around complex saddle points. Its ensemble average approximately becomes a direct sum of the average in each local distribution, where relative phases among them are dropped. We propose that by taking these phases into account through reweighting, we can solve the wrong convergence problem. However, this prescription may lead to a recurrence of the sign problem in the complex Langevin method for quantum many-body systems.}, journal={Nucl.Phys.B}, author={Hayata, Tomoya and Hidaka, Yoshimasa and Tanizaki, Yuya}, year={2016}, month={Oct}, pages={94–105} }
 @article{tanizaki_hidaka_hayata_2016, title={Lefschetz-thimble analysis of the sign problem in one-site fermion model}, volume={18}, url={http://inspirehep.net/record/1394683}, DOI={10.1088/1367-2630/18/3/033002}, abstractNote={The Lefschetz-thimble approach to path integrals is applied to a one-site model of electrons, i.e., the one-site Hubbard model. Since the one-site Hubbard model shows a non-analytic behavior at the zero temperature and its path integral expression has the sign problem, this toy model is a good testing ground for an idea or a technique to attack the sign problem. Semiclassical analysis using complex saddle points unveils the significance of interference among multiple Lefschetz thimbles to reproduce the non-analytic behavior by using the path integral. If the number of Lefschetz thimbles is insufficient, we found not only large discrepancies from the exact result, but also thermodynamic instabilities. Analyzing such singular behaviors semiclassically, we propose a criterion to identify the necessary number of Lefschetz thimbles. We argue that this interference of multiple saddle points is a key issue to understand the sign problem of the finite-density quantum chromodynamics.}, number={3}, journal={New J.Phys.}, publisher={IOP Publishing}, author={Tanizaki, Yuya and Hidaka, Yoshimasa and Hayata, Tomoya}, year={2016}, month={Mar}, pages={033002} }
 @inproceedings{tanizaki_hidaka_hayata_2016, place={Southampton, United Kingdom}, title={Lefschetz-thimble approach to the Silver Blaze problem of one-site fermion model}, volume={LATTICE2016}, url={http://inspirehep.net/record/1489199}, DOI={10.22323/1.256.0030}, abstractNote={The sign problem of finite-density QCD at the zero temperature becomes very severe if the quark chemical potential exceeds half of the pion mass. In order to understand its property, we consider the sign problem of the one-site fermion model appearing in its path-integral expression by using the Lefschetz-thimble method. We show that the original integration cycle becomes decomposed into multiple Lefschetz thimbles at a certain value of the fermion chemical potential, which would correspond to half of the pion mass of finite-density QCD. This triggers a fictitious phase transition on each Lefschetz thimble, and the interference of complex phases among them plays an important role for the correct description of the system. We also show that the complex Langevin method does not work in this situation.}, booktitle={PoS}, publisher={SISSA}, author={Tanizaki, Yuya and Hidaka, Yoshimasa and Hayata, Tomoya}, year={2016}, month={Sep}, pages={030} }
 @article{tanizaki_nishimura_kashiwa_2015, title={Evading the sign problem in the mean-field approximation through Lefschetz-thimble path integral}, volume={91}, url={http://inspirehep.net/record/1359295}, DOI={10.1103/PhysRevD.91.101701}, abstractNote={The fermion sign problem appearing in the mean-field approximation is considered, and the systematic computational scheme of the free energy is devised by using the Lefschetz-thimble method. We show that the Lefschetz-thimble method respects the reflection symmetry, which makes physical quantities manifestly real at any order of approximations using complex saddle points. The formula is demonstrated through the Airy integral as an example, and its application to the Polyakov-loop effective model of dense QCD is discussed in detail.}, number={10}, journal={Phys.Rev.D}, publisher={American Physical Society (APS)}, author={Tanizaki, Yuya and Nishimura, Hiromichi and Kashiwa, Kouji}, year={2015}, month={May}, pages={101701} }
 @article{mesterhazy_stockemer_tanizaki_2015, title={From quantum to classical dynamics: The relativistic $O(N)$ model in the framework of the real-time functional renormalization group}, volume={92}, url={http://inspirehep.net/record/1365098}, DOI={10.1103/PhysRevD.92.076001}, abstractNote={We investigate the transition from unitary to dissipative dynamics in the relativistic $O(N)$ vector model with the $\ensuremath{\lambda}{({\ensuremath{\varphi}}^{2})}^{2}$ interaction using the nonperturbative functional renormalization group in the real-time formalism. In thermal equilibrium, the theory is characterized by two scales, the interaction range for coherent scattering of particles and the mean free path determined by the rate of incoherent collisions with excitations in the thermal medium. Their competition determines the renormalization group flow and the effective dynamics of the model. Here we quantify the dynamic properties of the model in terms of the scale-dependent dynamic critical exponent $z$ in the limit of large temperatures and in $2\ensuremath{\le}d\ensuremath{\le}4$ spatial dimensions. We contrast our results to the behavior expected at vanishing temperature and address the question of the appropriate dynamic universality class for the given microscopic theory.}, number={7}, journal={Phys.Rev.D}, author={Mesterhazy, David and Stockemer, Jan H. and Tanizaki, Yuya}, year={2015}, month={Oct}, pages={076001} }
 @unpublished{mesterházy_stockemer_tanizaki_2015, title={From quantum to classical dynamics: The relativistic O(N) model in the framework of the real-time functional renormalization group}, url={http://inspirehep.net/record/1365098}, author={Mesterházy, David and Stockemer, Jan H. and Tanizaki, Yuya}, year={2015}, month={Apr} }
 @article{fukushima_tanizaki_2015, title={Hamilton dynamics for Lefschetz-thimble integration akin to the complex Langevin method}, volume={2015}, url={http://inspirehep.net/record/1385114}, DOI={10.1093/ptep/ptv152}, abstractNote={The Lefschetz thimble method, i.e., the integration along the steepest descent cycles, is an idea to evade the sign problem by complexifying the theory. We discuss that such steepest descent cycles can be identified as ground-state wave-functions of a supersymmetric Hamilton dynamics, which is described with a framework akin to the complex Langevin method. We numerically construct the wave-functions on a grid using a toy model and confirm their well-localized behavior.}, number={11}, journal={PTEP}, author={Fukushima, Kenji and Tanizaki, Yuya}, year={2015}, month={Nov}, pages={111A01} }
 @inproceedings{tanizaki_nishimura_kashiwa_2015, place={Kobe, Japan}, title={Lefschetz-thimble path integral for solving the mean-field sign problem}, volume={LATTICE2015}, url={http://inspirehep.net/record/1476940}, DOI={10.22323/1.251.0282}, abstractNote={The sign problem is a serious obstacle not only for the Monte Carlo method in lattice field theories, but also for the mean-field approximation in the effective models.The Lefschetz-thimble approach can be a key clue to understand these problems, and we show that the mean-field sign problem can be solved.}, booktitle={PoS}, publisher={SISSA}, author={Tanizaki, Yuya and Nishimura, Hiromichi and Kashiwa, Kouji}, year={2015}, month={Aug}, pages={282} }
 @article{tanizaki_2015, title={Lefschetz-thimble techniques for path integral of zero-dimensional O (n) sigma models}, volume={91}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84922570057&partnerID=MN8TOARS}, DOI={10.1103/PhysRevD.91.036002}, abstractNote={Zero-dimensional $O(n)$-symmetric sigma models are studied using the Picard-Lefschetz integration method in the presence of small symmetry-breaking perturbations. Because of approximate symmetry, downward flows turn out to show significant structures: They slowly travel along the set of pseudoclassical points, and branch into other directions so as to span middle-dimensional integration cycles. We propose an efficient way to find such slow motions for computing Lefschetz thimbles. In the limit of symmetry restoration, we figure out that only special combinations of Lefschetz thimbles can survive as convergent integration cycles: Other integrations become divergent due to noncompactness of the complexified group of symmetry. We also compute downward flows of $O(2)$-symmetric fermionic systems, and confirm that all of these properties are true also with fermions.}, number={3}, journal={Phys. Rev. D}, publisher={American Physical Society (APS)}, author={Tanizaki, Yuya}, year={2015}, pages={036002} }
 @article{kanazawa_tanizaki_2015, title={Structure of Lefschetz thimbles in simple fermionic systems}, volume={2015}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84924873080&partnerID=MN8TOARS}, DOI={10.1007/JHEP03(2015)044}, abstractNote={The Picard-Lefschetz theory offers a promising tool to solve the sign problem in QCD and other field theories with complex path-integral weight. In this paper the Lefschetz-thimble approach is examined in simple fermionic models which share some features with QCD. In zero-dimensional versions of the Gross-Neveu model and the Nambu-Jona-Lasinio model, we study the structure of Lefschetz thimbles and its variation across the chiral phase transition. We map out a phase diagram in the complex four-fermion coupling plane using a thimble decomposition of the path integral, and demonstrate an interesting link between anti-Stokes lines and Lee-Yang zeros. In the case of nonzero mass, it is shown that the approach to the chiral limit is singular because of intricate cancellation between competing thimbles, which implies the necessity to sum up multiple thimbles related by symmetry. We also consider a Chern-Simons theory with fermions in 0 + 1-dimension and show how Lefschetz thimbles solve the complex phase problem caused by a topological term. These prototypical examples would aid future application of this framework to bona fide QCD.}, number={3}, journal={J. High Energ. Phys.}, publisher={Springer Science \mathplus Business Media}, author={Kanazawa, Takuya and Tanizaki, Yuya}, year={2015}, pages={044} }
 @phdthesis{tanizaki_2015, title={Study on sign problem via Lefschetz-thimble path integral}, url={http://inspirehep.net/record/1635474}, DOI={10.15083/00073296}, school={Tokyo U.}, author={Tanizaki, Yuya}, year={2015}, month={Dec} }
 @article{tanizaki_2014, title={Fermionic functional renormalization group approach to Bose-Einstein condensation of dimers}, volume={2014}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84898490553&partnerID=MN8TOARS}, DOI={10.1093/ptep/ptu009}, abstractNote={Fermionic functional renormalization group (f-FRG) is applied to describe Bose-Einstein condensation (BEC) of dimers for a two-component fermionic system with attractive contact interaction. In order to describe the system of dimers without introducing auxiliary bosonic fields (bosonization), we propose a new exact evolution-equation of the effective action in f-FRG with an infrared regulator for the fermion vertex. Then we analyze its basic properties in details. We show explicitly that the critical temperature of the free Bose gas is obtained naturally by this method without bosonization. Methods to make systematic improvement from the deep BEC limit are briefly discussed.}, number={2}, journal={PTEP}, author={Tanizaki, Yuya}, year={2014}, pages={023A04} }
 @article{tanizaki_fejős_hatsuda_2014, title={Fermionic functional renormalization group approach to superfluid phase transition}, volume={2014}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84898483737&partnerID=MN8TOARS}, DOI={10.1093/ptep/ptu035}, abstractNote={Fermionic functional renormalization group (FRG) is applied to describe the superfluid phase transition of the two-component fermionic system with attractive contact interaction. Connection between the fermionic FRG approach and the conventional Bardeen-Cooper-Schrieffer (BCS) theory with Gorkov and Melik-Barkhudarov (GMB) correction are clarified in details in the weak coupling region by using the renormalization group flow of the fermionic four-point vertex with particle-particle and particle-hole scattering contributions. To go beyond the BCS+GMB theory, coupled FRG flow equations of the fermion self-energy and the four-point vertex are studied under an Ansatz concerning their frequency/momentum dependence. We found that the fermion self-energy turns out to be substantial even in the weak couping region, and the frequency dependence of the four-point vertex is essential to obtain the correct asymptotic-ultraviolet behavior of the flow for the self-energy. The superfluid transition temperature and the associated chemical potential are calculated in the region of negative scattering lengths.}, number={4}, journal={PTEP}, author={Tanizaki, Yuya and Fejős, Gergely and Hatsuda, Tetsuo}, year={2014}, pages={043I01} }
 @inproceedings{tanizaki_fejős_hatsuda_2014, title={Functional renormalization group approach to conventional theory of superfluidity and beyond}, volume={529}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84906690155&partnerID=MN8TOARS}, DOI={10.1088/1742-6596/529/1/012027}, abstractNote={Fermionic functional renormalization group (FRG) is applied to describe the superfluid phase transition of the two-component fermionic system with attractive contact interaction. Connection between the fermionic FRG approach and the Bardeen-Cooper- Schrieffer (BCS) theory with its Gorkov and Melik-Barkhudarov (GMB) correction is made clear, and the FRG flow of the fermion self-energy is also studied to go beyond the BCS+GMB theory. The superfluid transition temperature and the associated chemical potential are calculated in the region of the negative scattering length using fermionic FRG.}, number={1}, booktitle={Journal of Physics: Conference Series}, author={Tanizaki, Yuya and Fejős, Gergely and Hatsuda, Tetsuo}, year={2014}, pages={012027} }
 @inproceedings{tanizaki_2014, title={Many-Body Composite Bosons from the Viewpoint of Functional Renormalization}, volume={41}, url={http://inspirehep.net/record/1337529}, number={2}, booktitle={Bulg.J.Phys.}, author={Tanizaki, Yuya}, year={2014}, pages={180–186} }
 @inproceedings{many-body composite bosons from the viewpoint of functional renormalization_2014, url={http://www.bjp-bg.com/paper.php?id=698}, booktitle={Bulgarian Journal of Physics}, year={2014}, month={Oct} }
 @article{kashiwa_tanizaki_2014, title={Phase structure of SU (3) gauge-Higgs unification models at finite temperature}, volume={89}, url={http://www.scopus.com/inward/record.url?eid=2-s2.0-84903692266&partnerID=MN8TOARS}, DOI={10.1103/PhysRevD.89.116013}, abstractNote={Five-dimensional $SU(3)$ gauge-Higgs unification models are studied at finite temperature in the warped extra dimension ${S}^{1}/{\mathbb{Z}}_{2}$. In order to investigate the phase structure, we develop a technique to compute the one-loop effective potential with the nontrivial Polyakov loop phase and with the nontrivial Wilson line phase along the extra dimension. Effective potentials as functions of two gauge-field condensations are shown for several simple matter contents, including fundamental, sextet, and adjoint representational Dirac fermions. Possible extensions and applications of our formalism are also briefly discussed.}, number={11}, journal={Phys.Rev.D}, author={Kashiwa, Kouji and Tanizaki, Yuya}, year={2014}, pages={116013} }
 @article{tanizaki_koike_2014, title={Real-time path integral with Picard-Lefschetz theory and its applications to quantum tunneling}, volume={351}, url={http://dx.doi.org/10.1016/j.aop.2014.09.003}, DOI={10.1016/j.aop.2014.09.003}, abstractNote={Picard–Lefschetz theory is applied to path integrals of quantum mechanics, in order to compute real-time dynamics directly. After discussing basic properties of real-time path integrals on Lefschetz thimbles, we demonstrate its computational method in a concrete way by solving three simple examples of quantum mechanics. It is applied to quantum mechanics of a double-well potential, and quantum tunneling is discussed. We identify all of the complex saddle points of the classical action, and their properties are discussed in detail. However a big theoretical difficulty turns out to appear in rewriting the original path integral into a sum of path integrals on Lefschetz thimbles. We discuss generality of that problem and mention its importance. Real-time tunneling processes are shown to be described by those complex saddle points, and thus semi-classical description of real-time quantum tunneling becomes possible on solid ground if we could solve that problem.}, journal={Annals of Physics}, author={Tanizaki, Yuya and Koike, Takayuki}, year={2014}, month={Sep}, pages={250–274} }
 @article{tanizaki_2013, title={Flow equation of functional renormalization group for three-body scattering problems}, volume={2013}, url={http://inspirehep.net/record/1227948}, DOI={10.1093/ptep/ptt092}, abstractNote={Functional renormalization group (FRG) is applied to the three-body scattering problem in the two-component fermionic system with an attractive contact interaction. We establish a new and correct flow equation on the basis of FRG and show that our flow equation is consistent with integral equations obtained from the Dyson-Schwinger equation. In particular, the relation of our flow equation and the Skornyakov and Ter-Martirosyan equation for the atom-dimer scattering is made clear.}, number={11}, journal={Progress of Theoretical and Experimental Physics}, author={Tanizaki, Yuya}, year={2013}, month={Nov}, pages={113A01} }